In a manufacturing process of semiconductor devices, film-thickness information is monitored during polishing of a film that forms a front surface of a wafer. During polishing, pressures, applied to multiple zones on a back surface of the wafer, are manipulated to control a distribution of remaining film thickness. For example, Japanese laid-open patent publication No. 2008-503356 and International patent publication No. 2008/032753 disclose such a technique.
In this control operation of the distribution of remaining film thickness, it is important to correctly grasp an influence on a polishing rate resulting from a change in the pressure against the wafer back surface (e.g., characteristics including a dead time of a response, a response lag, a process gain which is a ratio of the polishing rate to the pressure) and to determine control parameters based on these characteristics. The control parameters are condition values that determine a controlling operation. For example, the control parameters include a proportional gain, an integral gain, and a derivative gain in PID control. In a model predictive control, the control parameters include a constant of proportionality in a prediction model and a response lag. It has been a conventional practice to use empirically-selected values as the control parameters, or estimate a part of the control parameters by polishing a sample wafer having the same structure as a product wafer, because there is a constraint in use of individual product wafers and there is a difficulty in measurement of the film thickness.
However, even if the same pressure is exerted on back surfaces of wafers, an actual polishing rate (or removal rate) may vary between wafers, due to variations in conditions of consumables, such as a polishing pad and a retaining ring, and a variation in material of the film to be polished. Moreover, even when polishing one wafer, the removal rate may vary as a result of a change in a characteristic of an exposed layer (e.g., oxidation), removal of surface steps (e.g., surface irregularity), or an increase in wafer temperature in a latter half of polishing.
Therefore, if constant control parameters are used for the polishing control operation, such control parameters may not be suited to current process characteristics at each point in time. As a result, manipulated variables, such as a change in the pressure, may be unsuitable, and controllability may be lowered.